Find the equation for the surface formed by rotating (x = 3*cos(y)) about the y axis.
Your answer must not contain radical symbols (square root signs).
To find the equation for the surface formed by rotating the curve (x = 3*cos(y)) about the y-axis, we can use the concept of cylindrical coordinates.
The Cartesian equation (x = 3*cos(y)) can be rewritten in terms of cylindrical coordinates as (x = ρ*cos(θ), y = y, z = ρ*sin(θ)), where ρ represents the radial distance from the origin, θ represents the angle in the x-y plane, and y is the same as in the original equation.
Rotating the curve about the y-axis means that we are rotating it in the x-z plane while keeping y constant. The cylindrical coordinates for this surface can be written as (ρ = x, θ = y, z = z).
To find the equation for the surface, we need to eliminate ρ and θ from the above equations. Starting with ρ = x, we can substitute the Cartesian equation (x = 3*cos(y)):
ρ = 3*cos(y)
Next, we substitute ρ*sin(θ) for z:
z = ρ*sin(θ) = x*sin(y)
Now, we have the equation for the surface formed by rotating (x = 3*cos(y)) about the y-axis:
z = x*sin(y)
Therefore, the equation for the surface formed by rotating (x = 3*cos(y)) about the y-axis is z = x*sin(y).